In my experiment, I want to test whether dogs are more likely to head directly to a goal. The data is in the form so that $0$ (degrees) is a heading to the goal, $-90^\circ$ is a heading to the left and $90^\circ$ would be heading to the right.

Experimental group (headings in degrees): 3,0,-7,-10,10,-1,13,15,-3,-2,6,6,5
Control group      (headings in degrees): -40,124,178,137,55,58,139,25,8,26,132,179,152

I want to test the hypothesis that in the experimental condition, the dogs are more accurate (closer to $0$). I thought a good way of testing accuracy was to have a null hypothesis that "variances will be equal in both conditions", although technically the variances in the experimental condition could be very small (so the dogs all head in the same position) but in the wrong direction (mean heading could be $50^\circ$, for example).

Either way, if I did want to test the hypothesis, I thought of doing a Brown-Forysthe test which is essentially (if I am right) an ANOVA which tests if the absolute deviations from the median differ. However, the variances of the groups differ HUGELY since the dogs in the experimental condition were more consistent. Would it therefore be more appropriate to use a unequal variances t-test instead of an ANOVA?

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    $\begingroup$ Hypotheses about variances would refer to precision rather than accuracy. If you truly want to test accuracy, then test whether the experimental group tends to be closer to zero degrees than the control group. $\endgroup$
    – whuber
    Nov 30, 2014 at 20:04

1 Answer 1


Variance alone isn't suitable, since you're trying to compare closeness to a particular location on the circle. You could have small variance but be nowhere near 0.

If you compare absolute deviation from target, you'd have two sets of values on $[0,\pi]$ (or $[0,180]$ if you prefer to work in degrees), for which you're interested in some general sense of 'closeness' that's not exactly a test for change in location or scale.

Presumably under the null the distributions of deviations from target would be identically distributed, in which case you might consider something like a Wilcoxon-Mann-Whitney.

The original data are of course circular, and you could assume some parametric distribution such the von Mises for each distribution, and construct some parametric comparison of deviation from zero under that assumption (which would have contributions due to deviation in $\mu$ from $0$ and also due to changes in $\kappa$).

You could also do some general test of a difference in distribution (a two-sample goodness of fit test on the circle), and then try to identify whether that's a change in "spread" vs a change in "location" vs some more general difference.


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